Optimum nuclear parton distributions are determined by an analysis of muon and electron deep inelastic scattering data. Assuming simple A dependence and polynomial functions of x and 1−x for nuclear modification of parton distributions, we determine the initial distributions by a χ 2 analysis. Although valence-quark distributions are relatively well determined except for the small-x region, ant...

We present an approach for the acceleration of the restarted Arnoldi iteration for the computation of a number of eigenvalues of the standard eigenproblem Ax = x. This study applies the Chebyshev polynomial to the restarted Arnoldi iteration and proves that it computes necessary eigenvalues with far less complexity than the QR method. We also discuss the dependence of the convergence rate of th...

Consider a polynomial Liénard system depending on three parameters a, b, c and with the following properties: (i) The origin is the unique equilibrium for all parameters. (ii). If a crosses zero, then the origin changes its stability, and a limit cycle bifurcates from the equilibrium. We investigate analytically this bifurcation in dependence on the parameters b and c and establish the existenc...

This paper investigates linear systems with polynomial dependence on time-invariant uncertainties constrained in the simplex via homogeneous parameter-dependent quadratic Lyapunov functions (HPD-QLFs). It is shown that a sufficient condition for establishing whether the system is either stable or unstable can be obtained by solving a generalized eigenvalue problem. Moreover, this condition is a...

State-of-the-art methods in convex and non-convex optimization employ higher-order derivative information, either implicitly or explicitly. We explore the limitations of higher-order optimization and prove that even for convex optimization, a polynomial dependence on the approximation guarantee and higher-order smoothness parameters is necessary. As a special case, we show Nesterov’s accelerate...

We define a class of generic CR submanifolds of C n of real codi-mension d, 1 ≤ d ≤ n − 1, called the Bloom-Graham model graphs, whose graphing functions are partially decoupled in their dependence on the variables in the real directions. We prove a global version of the Baouendi-Treves CR approximation theorem, for Bloom-Graham model graphs with a polynomial growth assumption on their graphing...

Abstract— We consider the inversion of perturbed linear operators on Hilbert space. Namely, we study linear operators that depend on a small parameter and are singular when the parameter is equal to zero. First we consider the af£ne dependence on the parameter. We treat subsequently the cases of bounded operators with closed range, bounded operators with non closed range, and densely de£ned and...

We have derived orbital basis sets from scattering theory. They are expressed as polynomial approximations to the energy dependence of a set of partial waves, in quantized form. The corresponding matrices, as well as the Hamiltonian and overlap matrices, are specified by the values on the energy mesh of the screened resolvent and its first energy derivative. These orbitals are a generalization ...

in this paper, rst a design is proposed for representing fuzzy polynomials withinput fuzzy and output fuzzy. then, we sketch a constructive proof for existenceof such polynomial which can be fuzzy interpolation polynomial in a set given ofdiscrete points rather than a fuzzy function. finally, to illustrate some numericalexamples are solved.